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The effects of periodic nonlinearity, intermodulation distortion, phase detection uncertainty and electrical cross-talk in a three-longitudinal-mode laser heterodyne Doppler interferometer (TLMI) displacement measurement system are presented. A frequency-path model consisting of three frequency components and two paths is also designed. As a result, there will be six frequency-path elements and 21 distinct interference terms. The periodic nonlinearity in the TLMI is mathematically modelled and simulated. Simulation results are compared with the typical two-mode heterodyne interferometer to confirm the designed model performance. The authors demonstrate that the nonlinearity of TLMI can be greatly reduced using the same compensation method as used in a two-frequency interferometer proposed by Hou et al.